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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math.optimization.univariate;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math.FunctionEvaluationException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math.MaxIterationsExceededException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math.analysis.UnivariateRealFunction;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math.optimization.GoalType;<a name="line.22"></a>
<FONT color="green">023</FONT>    <a name="line.23"></a>
<FONT color="green">024</FONT>    /**<a name="line.24"></a>
<FONT color="green">025</FONT>     * Implements Richard Brent's algorithm (from his book "Algorithms for<a name="line.25"></a>
<FONT color="green">026</FONT>     * Minimization without Derivatives", p. 79) for finding minima of real<a name="line.26"></a>
<FONT color="green">027</FONT>     * univariate functions.<a name="line.27"></a>
<FONT color="green">028</FONT>     *  <a name="line.28"></a>
<FONT color="green">029</FONT>     * @version $Revision: 799857 $ $Date: 2009-08-01 09:07:12 -0400 (Sat, 01 Aug 2009) $<a name="line.29"></a>
<FONT color="green">030</FONT>     * @since 2.0<a name="line.30"></a>
<FONT color="green">031</FONT>     */<a name="line.31"></a>
<FONT color="green">032</FONT>    public class BrentOptimizer extends AbstractUnivariateRealOptimizer {<a name="line.32"></a>
<FONT color="green">033</FONT>        <a name="line.33"></a>
<FONT color="green">034</FONT>        /**<a name="line.34"></a>
<FONT color="green">035</FONT>         * Golden section.<a name="line.35"></a>
<FONT color="green">036</FONT>         */<a name="line.36"></a>
<FONT color="green">037</FONT>        private static final double c = 0.5 * (3 - Math.sqrt(5));<a name="line.37"></a>
<FONT color="green">038</FONT>    <a name="line.38"></a>
<FONT color="green">039</FONT>        /**<a name="line.39"></a>
<FONT color="green">040</FONT>         * Construct a solver.<a name="line.40"></a>
<FONT color="green">041</FONT>         */<a name="line.41"></a>
<FONT color="green">042</FONT>        public BrentOptimizer() {<a name="line.42"></a>
<FONT color="green">043</FONT>            super(100, 1E-10);<a name="line.43"></a>
<FONT color="green">044</FONT>        }<a name="line.44"></a>
<FONT color="green">045</FONT>    <a name="line.45"></a>
<FONT color="green">046</FONT>        /** {@inheritDoc} */<a name="line.46"></a>
<FONT color="green">047</FONT>        public double optimize(final UnivariateRealFunction f, final GoalType goalType,<a name="line.47"></a>
<FONT color="green">048</FONT>                               final double min, final double max, final double startValue)<a name="line.48"></a>
<FONT color="green">049</FONT>            throws MaxIterationsExceededException, FunctionEvaluationException {<a name="line.49"></a>
<FONT color="green">050</FONT>            return optimize(f, goalType, min, max);<a name="line.50"></a>
<FONT color="green">051</FONT>        }<a name="line.51"></a>
<FONT color="green">052</FONT>        <a name="line.52"></a>
<FONT color="green">053</FONT>        /** {@inheritDoc} */<a name="line.53"></a>
<FONT color="green">054</FONT>        public double optimize(final UnivariateRealFunction f, final GoalType goalType,<a name="line.54"></a>
<FONT color="green">055</FONT>                               final double min, final double max)<a name="line.55"></a>
<FONT color="green">056</FONT>            throws MaxIterationsExceededException, FunctionEvaluationException {<a name="line.56"></a>
<FONT color="green">057</FONT>            clearResult();<a name="line.57"></a>
<FONT color="green">058</FONT>            return localMin(f, goalType, min, max, relativeAccuracy, absoluteAccuracy);<a name="line.58"></a>
<FONT color="green">059</FONT>        }<a name="line.59"></a>
<FONT color="green">060</FONT>        <a name="line.60"></a>
<FONT color="green">061</FONT>        /**<a name="line.61"></a>
<FONT color="green">062</FONT>         * Find the minimum of the function {@code f} within the interval {@code (a, b)}.<a name="line.62"></a>
<FONT color="green">063</FONT>         *<a name="line.63"></a>
<FONT color="green">064</FONT>         * If the function {@code f} is defined on the interval {@code (a, b)}, then<a name="line.64"></a>
<FONT color="green">065</FONT>         * this method finds an approximation {@code x} to the point at which {@code f}<a name="line.65"></a>
<FONT color="green">066</FONT>         * attains its minimum.&lt;br/&gt;<a name="line.66"></a>
<FONT color="green">067</FONT>         * {@code t} and {@code eps} define a tolerance {@code tol = eps |x| + t} and<a name="line.67"></a>
<FONT color="green">068</FONT>         * {@code f} is never evaluated at two points closer together than {@code tol}.<a name="line.68"></a>
<FONT color="green">069</FONT>         * {@code eps} should be no smaller than &lt;em&gt;2 macheps&lt;/em&gt; and preferable not<a name="line.69"></a>
<FONT color="green">070</FONT>         * much less than &lt;em&gt;sqrt(macheps)&lt;/em&gt;, where &lt;em&gt;macheps&lt;/em&gt; is the relative<a name="line.70"></a>
<FONT color="green">071</FONT>         * machine precision. {@code t} should be positive.<a name="line.71"></a>
<FONT color="green">072</FONT>         * @param f the function to solve<a name="line.72"></a>
<FONT color="green">073</FONT>         * @param goalType type of optimization goal: either {@link GoalType#MAXIMIZE}<a name="line.73"></a>
<FONT color="green">074</FONT>         * or {@link GoalType#MINIMIZE}<a name="line.74"></a>
<FONT color="green">075</FONT>         * @param a Lower bound of the interval<a name="line.75"></a>
<FONT color="green">076</FONT>         * @param b Higher bound of the interval<a name="line.76"></a>
<FONT color="green">077</FONT>         * @param eps Relative accuracy<a name="line.77"></a>
<FONT color="green">078</FONT>         * @param t Absolute accuracy<a name="line.78"></a>
<FONT color="green">079</FONT>         * @return the point at which the function is minimal.<a name="line.79"></a>
<FONT color="green">080</FONT>         * @throws MaxIterationsExceededException if the maximum iteration count<a name="line.80"></a>
<FONT color="green">081</FONT>         * is exceeded.<a name="line.81"></a>
<FONT color="green">082</FONT>         * @throws FunctionEvaluationException if an error occurs evaluating<a name="line.82"></a>
<FONT color="green">083</FONT>         * the function. <a name="line.83"></a>
<FONT color="green">084</FONT>         */<a name="line.84"></a>
<FONT color="green">085</FONT>        private double localMin(final UnivariateRealFunction f, final GoalType goalType,<a name="line.85"></a>
<FONT color="green">086</FONT>                                double a, double b, final double eps, final double t)<a name="line.86"></a>
<FONT color="green">087</FONT>            throws MaxIterationsExceededException, FunctionEvaluationException {<a name="line.87"></a>
<FONT color="green">088</FONT>            double x = a + c * (b - a);<a name="line.88"></a>
<FONT color="green">089</FONT>            double v = x;<a name="line.89"></a>
<FONT color="green">090</FONT>            double w = x;<a name="line.90"></a>
<FONT color="green">091</FONT>            double e = 0;<a name="line.91"></a>
<FONT color="green">092</FONT>            double fx = computeObjectiveValue(f, x);<a name="line.92"></a>
<FONT color="green">093</FONT>            if (goalType == GoalType.MAXIMIZE) {<a name="line.93"></a>
<FONT color="green">094</FONT>                fx = -fx;<a name="line.94"></a>
<FONT color="green">095</FONT>            }<a name="line.95"></a>
<FONT color="green">096</FONT>            double fv = fx;<a name="line.96"></a>
<FONT color="green">097</FONT>            double fw = fx;<a name="line.97"></a>
<FONT color="green">098</FONT>    <a name="line.98"></a>
<FONT color="green">099</FONT>            int count = 0;<a name="line.99"></a>
<FONT color="green">100</FONT>            while (count &lt; maximalIterationCount) {<a name="line.100"></a>
<FONT color="green">101</FONT>                double m = 0.5 * (a + b);<a name="line.101"></a>
<FONT color="green">102</FONT>                double tol = eps * Math.abs(x) + t;<a name="line.102"></a>
<FONT color="green">103</FONT>                double t2 = 2 * tol;<a name="line.103"></a>
<FONT color="green">104</FONT>    <a name="line.104"></a>
<FONT color="green">105</FONT>                // Check stopping criterion.<a name="line.105"></a>
<FONT color="green">106</FONT>                if (Math.abs(x - m) &gt; t2 - 0.5 * (b - a)) {<a name="line.106"></a>
<FONT color="green">107</FONT>                    double p = 0;<a name="line.107"></a>
<FONT color="green">108</FONT>                    double q = 0;<a name="line.108"></a>
<FONT color="green">109</FONT>                    double r = 0;<a name="line.109"></a>
<FONT color="green">110</FONT>                    double d = 0;<a name="line.110"></a>
<FONT color="green">111</FONT>                    double u = 0;<a name="line.111"></a>
<FONT color="green">112</FONT>    <a name="line.112"></a>
<FONT color="green">113</FONT>                    if (Math.abs(e) &gt; tol) { // Fit parabola.<a name="line.113"></a>
<FONT color="green">114</FONT>                        r = (x - w) * (fx - fv);<a name="line.114"></a>
<FONT color="green">115</FONT>                        q = (x - v) * (fx - fw);<a name="line.115"></a>
<FONT color="green">116</FONT>                        p = (x - v) * q - (x - w) * r;<a name="line.116"></a>
<FONT color="green">117</FONT>                        q = 2 * (q - r);<a name="line.117"></a>
<FONT color="green">118</FONT>    <a name="line.118"></a>
<FONT color="green">119</FONT>                        if (q &gt; 0) {<a name="line.119"></a>
<FONT color="green">120</FONT>                            p = -p;<a name="line.120"></a>
<FONT color="green">121</FONT>                        } else {<a name="line.121"></a>
<FONT color="green">122</FONT>                            q = -q;<a name="line.122"></a>
<FONT color="green">123</FONT>                        }<a name="line.123"></a>
<FONT color="green">124</FONT>    <a name="line.124"></a>
<FONT color="green">125</FONT>                        r = e;<a name="line.125"></a>
<FONT color="green">126</FONT>                        e = d;<a name="line.126"></a>
<FONT color="green">127</FONT>                    }<a name="line.127"></a>
<FONT color="green">128</FONT>    <a name="line.128"></a>
<FONT color="green">129</FONT>                    if (Math.abs(p) &lt; Math.abs(0.5 * q * r) &amp;&amp;<a name="line.129"></a>
<FONT color="green">130</FONT>                        (p &lt; q * (a - x)) &amp;&amp; (p &lt; q * (b - x))) { // Parabolic interpolation step.<a name="line.130"></a>
<FONT color="green">131</FONT>                        d = p / q;<a name="line.131"></a>
<FONT color="green">132</FONT>                        u = x + d;<a name="line.132"></a>
<FONT color="green">133</FONT>    <a name="line.133"></a>
<FONT color="green">134</FONT>                        // f must not be evaluated too close to a or b.<a name="line.134"></a>
<FONT color="green">135</FONT>                        if (((u - a) &lt; t2) || ((b - u) &lt; t2)) {<a name="line.135"></a>
<FONT color="green">136</FONT>                            d = (x &lt; m) ? tol : -tol;<a name="line.136"></a>
<FONT color="green">137</FONT>                        }<a name="line.137"></a>
<FONT color="green">138</FONT>                    } else { // Golden section step.<a name="line.138"></a>
<FONT color="green">139</FONT>                        e = ((x &lt; m) ? b : a) - x;<a name="line.139"></a>
<FONT color="green">140</FONT>                        d = c * e;<a name="line.140"></a>
<FONT color="green">141</FONT>                    }<a name="line.141"></a>
<FONT color="green">142</FONT>    <a name="line.142"></a>
<FONT color="green">143</FONT>                    // f must not be evaluated too close to a or b.<a name="line.143"></a>
<FONT color="green">144</FONT>                    u = x + ((Math.abs(d) &gt; tol) ? d : ((d &gt; 0) ? tol : -tol));<a name="line.144"></a>
<FONT color="green">145</FONT>                    double fu = computeObjectiveValue(f, u);<a name="line.145"></a>
<FONT color="green">146</FONT>                    if (goalType == GoalType.MAXIMIZE) {<a name="line.146"></a>
<FONT color="green">147</FONT>                        fu = -fu;<a name="line.147"></a>
<FONT color="green">148</FONT>                    }<a name="line.148"></a>
<FONT color="green">149</FONT>    <a name="line.149"></a>
<FONT color="green">150</FONT>                    // Update a, b, v, w and x.<a name="line.150"></a>
<FONT color="green">151</FONT>                    if (fu &lt;= fx) {<a name="line.151"></a>
<FONT color="green">152</FONT>                        if (u &lt; x) {<a name="line.152"></a>
<FONT color="green">153</FONT>                            b = x;<a name="line.153"></a>
<FONT color="green">154</FONT>                        } else {<a name="line.154"></a>
<FONT color="green">155</FONT>                            a = x;<a name="line.155"></a>
<FONT color="green">156</FONT>                        }<a name="line.156"></a>
<FONT color="green">157</FONT>                        v = w;<a name="line.157"></a>
<FONT color="green">158</FONT>                        fv = fw;<a name="line.158"></a>
<FONT color="green">159</FONT>                        w = x;<a name="line.159"></a>
<FONT color="green">160</FONT>                        fw = fx;<a name="line.160"></a>
<FONT color="green">161</FONT>                        x = u;<a name="line.161"></a>
<FONT color="green">162</FONT>                        fx = fu;<a name="line.162"></a>
<FONT color="green">163</FONT>                    } else {<a name="line.163"></a>
<FONT color="green">164</FONT>                        if (u &lt; x) {<a name="line.164"></a>
<FONT color="green">165</FONT>                            a = u;<a name="line.165"></a>
<FONT color="green">166</FONT>                        } else {<a name="line.166"></a>
<FONT color="green">167</FONT>                            b = u;<a name="line.167"></a>
<FONT color="green">168</FONT>                        }<a name="line.168"></a>
<FONT color="green">169</FONT>                        if ((fu &lt;= fw) || (w == x)) {<a name="line.169"></a>
<FONT color="green">170</FONT>                            v = w;<a name="line.170"></a>
<FONT color="green">171</FONT>                            fv = fw;<a name="line.171"></a>
<FONT color="green">172</FONT>                            w = u;<a name="line.172"></a>
<FONT color="green">173</FONT>                            fw = fu;<a name="line.173"></a>
<FONT color="green">174</FONT>                        } else if ((fu &lt;= fv) || (v == x) || (v == w)) {<a name="line.174"></a>
<FONT color="green">175</FONT>                            v = u;<a name="line.175"></a>
<FONT color="green">176</FONT>                            fv = fu;<a name="line.176"></a>
<FONT color="green">177</FONT>                        }<a name="line.177"></a>
<FONT color="green">178</FONT>                    }<a name="line.178"></a>
<FONT color="green">179</FONT>                } else { // termination<a name="line.179"></a>
<FONT color="green">180</FONT>                    setResult(x, (goalType == GoalType.MAXIMIZE) ? -fx : fx, count);<a name="line.180"></a>
<FONT color="green">181</FONT>                    return x;<a name="line.181"></a>
<FONT color="green">182</FONT>                }<a name="line.182"></a>
<FONT color="green">183</FONT>    <a name="line.183"></a>
<FONT color="green">184</FONT>                ++count;<a name="line.184"></a>
<FONT color="green">185</FONT>            }<a name="line.185"></a>
<FONT color="green">186</FONT>    <a name="line.186"></a>
<FONT color="green">187</FONT>            throw new MaxIterationsExceededException(maximalIterationCount);<a name="line.187"></a>
<FONT color="green">188</FONT>    <a name="line.188"></a>
<FONT color="green">189</FONT>        }<a name="line.189"></a>
<FONT color="green">190</FONT>    <a name="line.190"></a>
<FONT color="green">191</FONT>    }<a name="line.191"></a>




























































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